Left invariant vector field under a gauge transformation

[nigelscott]

Homework Statement

For a left invariant vector field γ(t) = exp(tv). For a gauge transformation t -> t(x^μ). Intuitively, what happens to the LIVF in the latter case? Is it just displaced to a different point in spacetime or something else?

Homework Equations

The Attempt at a Solution

 

[member 553083]

When a gauge transformation is applied, the LIVF is merely displaced to a different point in spacetime. This is because the vector field is left invariant and therefore, it must be displaced to another point in space-time in order to remain invariant.